Preheat your oven to 350°F (175°C) and prepare two 6- or 7-inch greased and floured cake pans lined with parchment paper.

In a small bowl, combine your choice of milk with apple cider vinegar or lemon juice and let it rest for at least 5 minutes.

In a food processor, pulse the ground pistachios and sugar together until finely blended. Whisk flour, baking powder, and salt in a separate bowl, then fold in the pistachio-sugar mixture.

In a large bowl, whisk together the prepared buttermilk, olive oil, vanilla extract, and almond extract until smooth.

Gently fold the dry ingredients into the wet mixture until just combined.

Divide the batter between the prepared pans and bake for 25-30 minutes or until a toothpick comes out clean.

Remove the cakes from the oven, cool in the pans for around 10 minutes, then transfer to wire racks to cool completely.

Beat room temperature butter until creamy, then add blackberry preserves and powdered sugar gradually, mixing well. Stir in dried thyme.

Layer cooled cakes with buttercream and blackberry preserves between them, covering the entire cake with remaining buttercream.

Slice and serve your cake chilled or at room temperature, optionally pairing it with whipped cream or vanilla ice cream.